1. For what value of a ,
is a singular matrix?
2. Find the equation of tangent to the curve √x + √y = a at the point ![](images/2.jpg)
3. If
and B= [ -2 -1 -4 ] find AB.
4. If A is a matrix of order 3 and |A| = 8 then find the value of |A dv A |.
5. Without expanding evaluate the determinant ![](images/4.jpg)
SECTION B
6. Prove that ![](images/5.jpg)
7. Find the points on the curve 6 y2 = x3 where normal to the curve makes equal intercepts with the axes.
8. Show that Matrix
show that : A2 - 4A - 5I3 = 0 and hence find A-1.
9. Show that the semi vertical angle of a cone of given total surface area and maximum volume is ![](images/7.jpg)
10. Prove that ![](images/8.jpg)
11. Using elementary operations, find the inverse of matrix ![](images/9.jpg)
SECTION C
12. Determine the product
and use it solve the system of equations: x – y + z = 4; x – 2y – 2z = 9 and 2x + y + 3z = 1.
OR
Using elementary transformations, find the inverse of the matrix : ![](images/11.jpg)
13. If the length of the trapezium, other than base is equal to 10 cm each, then find the area of trapezium when it is maximum.
OR
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r / 3 .
14. Show that
.